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Omni-MATH / The following construction is used for training astronauts:

Problem

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problem

The following construction is used for training astronauts: A circle C2C_2 of radius 2R2R rolls along the inside of another, fixed circle C1C_1 of radius nRnR, where nn is an integer greater than 22. The astronaut is fastened to a third circle C3C_3 of radius RR which rolls along the inside of circle C2C_2 in such a way that the touching point of the circles C2C_2 and C3C_3 remains at maximum distance from the touching point of the circles C1C_1 and C2C_2 at all times. How many revolutions (relative to the ground) does the astronaut perform together with the circle C3C_3 while the circle C2C_2 completes one full lap around the inside of circle C1C_1?
Plain-text mathematical notation (without MathML)
The following construction is used for training astronauts:
A circle C₂ of radius 2R rolls along the inside of another, fixed circle C₁ of radius nR, where n is an integer greater than 2. The astronaut is fastened to a third circle C₃ of radius R which rolls along the inside of circle C₂ in such a way that the touching point of the circles C₂ and C₃ remains at maximum distance from the touching point of the circles C₁ and C₂ at all times. How many revolutions (relative to the ground) does the astronaut perform together with the circle C₃ while the circle C₂ completes one full lap around the inside of circle C₁?
Original LaTeX notation
The following construction is used for training astronauts:
A circle $C_2$ of radius $2R$ rolls along the inside of another, fixed circle $C_1$ of radius $nR$, where $n$ is an integer greater than $2$. The astronaut is fastened to a third circle $C_3$ of radius $R$ which rolls along the inside of circle $C_2$ in such a way that the touching point of the circles $C_2$ and $C_3$ remains at maximum distance from the touching point of the circles $C_1$ and $C_2$ at all times. How many revolutions (relative to the ground) does the astronaut perform together with the circle $C_3$ while the circle $C_2$ completes one full lap around the inside of circle $C_1$?

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Source and history

task_id
363c954f-6b3c-5ebf-9d94-29a17c067214
task_key
test--363c954f-6b3c-5ebf-9d94-29a17c067214
task_revision_id
1
config / split
/ test

Official source

initial import